Find sets of parametric equations and symmetric equations of the line that passes through the two...
7. (-/1 Points) DETAILS LARCALC11 11.R.037. Find sets of parametric equations and symmetric equations of the line that passes through the two points. (For the line, write the direction numbers as integers.) (7, 0,5), (10, 11, 9) (a) Find sets of parametric equations. (Enter your answer as a comma-separated list of equations in terms of x, y, z, and t.) (b) Find sets of symmetric equations. *57 - 11 3+5 0 - 7x + 3 = 11y = -5z +...
24. Find the parametric and symmetric equations of the line that passes through the point (2, 1,-3) and is perpendicular to the planex+2y+2- 13. 14 marks] 25. Find the following quantities: 14 marks] a. (1+2)8- 5-5 b 23 (52 -1+i
(a) Find symmetric equations for the line that passes through the point (2, -2, 8) and is parallel to the vector (-1, 3,-4). -(x + 2) = 3(y-2) = -4(2 + 8). Ox+2-472.28 2-8 -4 -(x - 2) = 3(y + 2) = -4(2-8). *+2.1;2-28 (b) Find the points in which the required line in part (a) intersects the coordinate planes. point of intersection with xy-plane point of intersection with yz-plane point of intersection with xz plane
(a) Find symmetric equations for the line that passes through the point (4, -2, 6) and is parallel to the vector (-1, 3, -4) x+ 4-Y+ 2 3 z-6 -4 -(x +4) 3(y 2)-4(z +6). y+2 z-6 3 -(x-4) 3(y +2) -4(z- 6). o4-2-116 = Y - 2-z+6 3 (b) Find the points in which the required line in part (a) intersects the coordinate planes. 5 ,5,0 x ) point of intersection with xy-plane 10 7 point of intersection with...
1:34 Find the parametric equations of the line in Rthat passes through the points (2,4, 1) and (-3, -2,-4). (A) x 25t y 6 6 (B) x 2-5t y 4 6t (C) x -3-5t y 4 6t (D) х--2-t y 6-6t y 6-6t (G) x 2 -5t y 4 6 Problem 45
L2 2 7 2. Find parametric and symmetric equations for the line through (2, 1,0) and perpendicular to both i +j and j+k. Dind +
5. Find parametric equations for the line through the point (0, 1,2) that is orthogonal to the line x = 1 + t, y 1-t, 2t, and intersects this line. (Hint: Try drawing this scenario in two dimensions, ie. draw two orthogonal lines and a point on each line away from the intersection. How would you find the direction vector?)
Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x = 4 In(t), y = 6/t, z = t4; (0,6, 1) x(t), y(t), z(t) = X
find parametric equations for the tangent line to the curve with the given parametric equations at the specified point. x=10cost, y=10sint, z=8cos2t; (5sqrt3,5,4)
please answer question 16 and 17 17. Find the equation of a plane that passes through the points (15,5, 2), (6, 2, 1) and (10,3, 2). Does the point (-2,-5, -3) lie on the plane? [5 marks) 16. Find the equation of a line through the point (2, -3, 1) in a direction orthogonal to the line *+1 Y-1.2+2. Give your answer in both parametric and 3 5 symmetric form. [4 marks) 2